Comparing Fractions
Use a common denominator or cross-multiplication to compare.
Key idea
Use a common denominator or cross-multiplication to compare.
In depth
With the same denominator, the bigger numerator is bigger. Otherwise convert to a common denominator or cross-multiply: a/b < c/d exactly when ad < bc.
Worked example
3/5 vs 2/3: 3×3 = 9 and 2×5 = 10, so 3/5 < 2/3.
Formula
Real-world uses
- Deciding which mortgage rate or phone plan is better
- Judging which portion of a task is larger
Common mistake
Thinking a bigger denominator means a bigger fraction. 1/8 is smaller than 1/4.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Comparing Fractions?
Use a common denominator or cross-multiplication to compare. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Comparing Fractions?
The key formula is a/b < c/d ⇔ ad < bc.
Where is Comparing Fractions used in real life?
Real-world examples: Deciding which mortgage rate or phone plan is better; Judging which portion of a task is larger.
What should I learn before Comparing Fractions?
Make sure you are comfortable with Simplifying Fractions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Comparing Fractions?
Thinking a bigger denominator means a bigger fraction. 1/8 is smaller than 1/4.
How can I practise Comparing Fractions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Comparing Fractions?
Move on to Adding Fractions next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.